Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 2, 268-294

NONPARAMETRIC ESTIMATION OF JUMP SURFACE

By

PEIHUA QUI, The Ohio State University, Columbus

SUMMARY. In this paper, we discuss estimation of bivariate jump regression functions. An a.s. consistent estimator of the jump location curve is suggested. This estimator is based on difference of two one-sided kernel smoothers. A rotation transformation is used. We consider an ideal case that the jump location curve has an explicit function form first and the generalise it to a more general case that the explicit form does not exit. Comparing to some existing methods on this topic, mainly to the edge detection methods in image processing literature, our method uses less conditions on the design points and on the underlying regression function. So it is expected to find more applications.

AMS (1991) subject classification. 62G08, 68U10, 62A25, 62H05.

Key words and phrases. Jump regression function, difference kernel estimator, rotation transformation, uniformly a.s. consistent, image processing, edge detection.

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